Chapter 4, Problem 9PT

To determine

To find: The linear equation in slope-intercept form and the time required to paint a room measuring 750 square ft.

Answer to Problem 9PT

The linear equation in slope-intercept form is $y=\frac{13}{10}x+30$ and the time required to paint a room measuring 750 square ft is 1005 minutes.

Explanation of Solution

Given information: A table given where the room size is shown in square feet and the time taken to paint the room in minutes. Two points $(100,160)$ and $(500,680)$ given to find the equation in slope intercept form and given a room with measuring 750 square ft.

Room Size	100	150	200	400	500
Painting time	160	220	270	500	680

Calculation:

The two points given here are $(100,160)$ and $(500,680)$ .

  $\therefore$ Slope (m) = $\frac{y_2-y_1}{x_2-x_1}=\frac{680-160}{500-100}$ = $\frac{520}{400}=\frac{13}{10}$

The equation in slope-intercept form is $y=mx+b$

We can write it as, $y=\frac{13}{10}x+b$ , as m = $\frac{13}{10}$ .

It passes through the point $(100,160)$ .

  $\therefore$ We will get,

  $\begin{array}{l}160=\frac{13}{10}(100)+b\\ \Rightarrow 160=13(10)+b\\ \Rightarrow 160=130+b\\ \Rightarrow b=160-130\\ \Rightarrow b=30\end{array}$

So, the equation in slope-intercept form is $y=\frac{13}{10}x+30$ .

A room given with measuring 750 square ft, so we will plug in x = 750.

We will get,

  $\begin{array}{l}y=\frac{13}{10}(750)+30\\ \Rightarrow y=13(75)+30\\ \Rightarrow y=975+30\\ \Rightarrow y=1005\end{array}$

So, the time required to paint a 750 square ft room is 1005 minutes.